Subgroups — #27592491

Order 13568.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283005	C₂	1	1	yes	maximal, characteristic
2	#20283000	C₂	1	1	yes	maximal, characteristic, complemented
3	#20282478	C₂	1	1	yes	maximal, characteristic, complemented
4	#20282341	C₂	1	1	yes	maximal, characteristic, complemented
5	#20282223	C₂	1	1	yes	maximal, characteristic, complemented
6	#20282156	C₂	1	1	yes	maximal, characteristic, complemented
7	#20282140	C₂	1	1	yes	maximal, characteristic, complemented
8	#20282131	C₂	1	1	yes	maximal, characteristic, complemented
9	#20282054	C₂	1	1	yes	maximal, characteristic, complemented
10	#20281903	C₂	1	1	yes	maximal, characteristic, complemented
11	#20281806	C₂	1	1	yes	maximal, characteristic, complemented
12	#20281690	C₂	1	1	yes	maximal, characteristic, complemented
13	#20281567	C₂	1	1	yes	maximal, characteristic, complemented
14	#20281553	C₂	1	1	yes	maximal, characteristic, complemented
15	#20281287	C₂	1	1	yes	maximal, characteristic, complemented
16	#20281215	C₂	1	1	yes	maximal, characteristic, complemented
17	#20281140	C₂	1	1	yes	maximal, characteristic, complemented
18	#20280998	C₂	1	1	yes	maximal, characteristic, complemented
19	#20280532	C₂	1	1	yes	maximal, characteristic, complemented
20	#20280497	C₂	1	1	yes	maximal, characteristic, complemented
21	#20279873	C₂	1	1	yes	maximal, characteristic, complemented
22	#20279096	C₂	1	1	yes	maximal, characteristic, complemented
23	#20279045	C₂	1	1	yes	maximal, characteristic, complemented
24	#20278960	C₂	1	1	yes	maximal, characteristic, complemented
25	#20278840	C₂	1	1	yes	maximal, characteristic
26	#20278418	C₂	1	1	yes	maximal, characteristic, complemented
27	#20278166	C₂	1	1	yes	maximal, characteristic, complemented
28	#20277445	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277348	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16810498	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2534	C₂	1	1	yes	maximal, characteristic
32	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic
33	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13133210	C₂²	1	1	yes	characteristic
35	C₂×#13133204	C₂²	1	1	yes	characteristic
36	C₂×#13133198	C₂²	1	1	yes	characteristic
37	C₂×#13133198	C₂²	1	1	yes	characteristic
38	C₂×#13133196	C₂²	1	1	yes	characteristic
39	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13133194	C₂²	1	1	yes	characteristic
41	C₂×#13133194	C₂²	1	1	yes	characteristic
42	C₂×#13133194	C₂²	1	1	yes	characteristic
43	C₂×#13133194	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
47	C₅₃⋊#401	C₂²	1	1	yes	characteristic, complemented
48	#16810565	C₂²	1	1	yes	characteristic, complemented
49	#16810565	C₂²	1	1	yes	characteristic, complemented
50	#16810565	C₂²	1	1	yes	characteristic, complemented
51	#16810564	C₂²	1	1	yes	characteristic, complemented
52	#16810563	C₂²	1	1	yes	characteristic, complemented
53	#16810562	C₂²	1	1	yes	characteristic, complemented
54	#16810562	C₂²	1	1	yes	characteristic, complemented
55	#16810561	C₂²	1	1	yes	characteristic, complemented
56	#16810561	C₂²	1	1	yes	characteristic, complemented
57	#16810559	C₂²	1	1	yes	characteristic, complemented
58	#16810559	C₂²	1	1	yes	characteristic, complemented
59	#16810557	C₂²	1	1	yes	characteristic, complemented
60	#16810557	C₂²	1	1	yes	characteristic, complemented
61	#16810557	C₂²	1	1	yes	characteristic, complemented
62	#16810557	C₂²	1	1	yes	characteristic, complemented
63	#16810556	C₂²	1	1	yes	characteristic, complemented
64	#16810556	C₂²	1	1	yes	characteristic, complemented
65	#16810555	C₂²	1	1	yes	characteristic, complemented
66	#16810555	C₂²	1	1	yes	characteristic, complemented
67	#16810553	C₂²	1	1	yes	characteristic, complemented
68	#16810553	C₂²	1	1	yes	characteristic, complemented
69	#16810551	C₂²	1	1	yes	characteristic
70	#16810551	C₂²	1	1	yes	characteristic
71	#16810548	C₂²	1	1	yes	characteristic
72	#16810548	C₂²	1	1	yes	characteristic
73	#16810548	C₂²	1	1	yes	characteristic
74	#16810548	C₂²	1	1	yes	characteristic
75	#16810548	C₂²	1	1	yes	characteristic, complemented
76	#16810548	C₂²	1	1	yes	characteristic, complemented
77	#16810548	C₂²	1	1	yes	characteristic, complemented
78	#16810546	C₂²	1	1	yes	characteristic
79	#16810546	C₂²	1	1	yes	characteristic, complemented
80	#16810546	C₂²	1	1	yes	characteristic, complemented
81	#16810544	C₂²	1	1	yes	characteristic, complemented
82	#16810544	C₂²	1	1	yes	characteristic, complemented
83	#16810544	C₂²	1	1	yes	characteristic, complemented
84	#16810544	C₂²	1	1	yes	characteristic, complemented
85	#16810537	C₂²	1	1	yes	characteristic
86	#16810537	C₂²	1	1	yes	characteristic
87	#16810535	C₂²	1	1	yes	characteristic
88	#16810535	C₂²	1	1	yes	characteristic
89	#16810535	C₂²	1	1	yes	characteristic
90	#16810535	C₂²	1	1	yes	characteristic, complemented
91	#16810529	C₂²	1	1	yes	characteristic, complemented
92	#16810528	C₂²	1	1	yes	characteristic, complemented
93	#16810527	C₂²	1	1	yes	characteristic, complemented
94	#16810527	C₂²	1	1	yes	characteristic, complemented
95	#16810526	C₂²	1	1	yes	characteristic
96	#16810522	C₂²	1	1	yes	characteristic, complemented
97	#16810521	C₂²	1	1	yes	characteristic, complemented
98	#16810519	C₂²	1	1	yes	characteristic, complemented
99	#16810518	C₂²	1	1	yes	characteristic, complemented
100	#16810518	C₂²	1	1	yes	characteristic, complemented
101	#16810517	C₂²	1	1	yes	characteristic
102	#16810517	C₂²	1	1	yes	characteristic
103	#16810517	C₂²	1	1	yes	characteristic
104	#16810517	C₂²	1	1	yes	characteristic
105	#16810517	C₂²	1	1	yes	characteristic
106	#16810517	C₂²	1	1	yes	characteristic
107	#16810517	C₂²	1	1	yes	characteristic
108	#16810517	C₂²	1	1	yes	characteristic, complemented
109	#16810517	C₂²	1	1	yes	characteristic, complemented
110	#16810516	C₂²	1	1	yes	characteristic
111	#16810516	C₂²	1	1	yes	characteristic, complemented
112	#16810516	C₂²	1	1	yes	characteristic, complemented
113	#16810511	C₂²	1	1	yes	characteristic
114	#16810510	C₂²	1	1	yes	characteristic, complemented
115	#16810509	C₂²	1	1	yes	characteristic, complemented
116	#16810509	C₂²	1	1	yes	characteristic, complemented
117	#16810508	C₂²	1	1	yes	characteristic, complemented
118	#16810508	C₂²	1	1	yes	characteristic, complemented
119	#16810508	C₂²	1	1	yes	characteristic, complemented
120	#16810505	C₂²	1	1	yes	characteristic, complemented
121	#16810504	C₂²	1	1	yes	characteristic, complemented
122	#16810504	C₂²	1	1	yes	characteristic, complemented
123	#16810503	C₂²	1	1	yes	characteristic
124	#16810503	C₂²	1	1	yes	characteristic
125	#16810503	C₂²	1	1	yes	characteristic
126	#16810503	C₂²	1	1	yes	characteristic
127	#16810503	C₂²	1	1	yes	characteristic
128	#16810503	C₂²	1	1	yes	characteristic
129	#16810498	C₂²	1	1	yes	characteristic
130	#16810498	C₂²	1	1	yes	characteristic
131	#16810498	C₂²	1	1	yes	characteristic
132	#16810498	C₂²	1	1	yes	characteristic
133	#16810498	C₂²	1	1	yes	characteristic
134	#16810498	C₂²	1	1	yes	characteristic
135	#16810498	C₂²	1	1	yes	characteristic
136	#16810498	C₂²	1	1	yes	characteristic
137	#16810498	C₂²	1	1	yes	characteristic
138	#16810498	C₂²	1	1	yes	characteristic
139	#16810498	C₂²	1	1	yes	characteristic
140	#16810498	C₂²	1	1	yes	characteristic
141	#16810495	C₂²	1	1	yes	characteristic
142	#16810495	C₂²	1	1	yes	characteristic
143	#16810495	C₂²	1	1	yes	characteristic
144	#16810495	C₂²	1	1	yes	characteristic
145	#16810495	C₂²	1	1	yes	characteristic
146	#16810495	C₂²	1	1	yes	characteristic
147	#16810495	C₂²	1	1	yes	characteristic
148	#16810495	C₂²	1	1	yes	characteristic
149	#16810492	C₂²	1	1	yes	characteristic, complemented
150	#16810491	C₂²	1	1	yes	characteristic, complemented
151	#16810490	C₂²	1	1	yes	characteristic, complemented
152	#16810489	C₂²	1	1	yes	characteristic, complemented
153	#16810488	C₂²	1	1	yes	characteristic, complemented
154	#16810486	C₂²	1	1	yes	characteristic
155	#16810486	C₂²	1	1	yes	characteristic
156	#16810486	C₂²	1	1	yes	characteristic, complemented
157	#16810484	C₂²	1	1	yes	characteristic
158	#16810484	C₂²	1	1	yes	characteristic
159	#16810483	C₂²	1	1	yes	characteristic, complemented
160	#16810483	C₂²	1	1	yes	characteristic, complemented
161	#16810481	C₂²	1	1	yes	characteristic
162	#16810481	C₂²	1	1	yes	characteristic
163	#16810481	C₂²	1	1	yes	characteristic
164	#16810481	C₂²	1	1	yes	characteristic
165	#16810479	C₂²	1	1	yes	characteristic
166	#16810479	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
169	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
170	C₂×#13133124	C₂²	1	1	yes	characteristic
171	C₂×#13133124	C₂²	1	1	yes	characteristic
172	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
173	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
174	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
175	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
176	C₅₃×#396	C₂²	1	1	yes	characteristic
177	C₅₃×#396	C₂²	1	1	yes	characteristic
178	C₅₃×#394	C₂²	1	1	yes	characteristic
179	C₅₃×#394	C₂²	1	1	yes	characteristic
180	C₅₃×#388	C₂²	1	1	yes	characteristic
181	C₅₃×#388	C₂²	1	1	yes	characteristic
182	C₅₃×#386	C₂²	1	1	yes	characteristic
183	C₅₃×#386	C₂²	1	1	yes	characteristic
184	C₅₃×#381	C₂²	1	1	yes	characteristic
185	C₅₃×#380	C₂²	1	1	yes	characteristic
186	C₅₃×#379	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂³×Dic₅₃	—	4	2	no	—
191	C₂³×Dic₅₃	—	4	2	no	—
192	C₂³×Dic₅₃	—	4	2	no	—
193	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
194	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
195	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
196	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
197	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
198	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
199	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
200	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
201	#13133216	—	4	2	no	—
202	#13133210	—	4	2	no	—
203	#13133204	—	4	2	no	—
204	#13133198	—	4	2	no	—
205	#13133198	—	4	2	no	—
206	#13133196	—	2	4	no	—
207	#13133196	—	4	2	no	—
208	#13133194	—	4	2	no	—
209	#13133194	—	4	2	no	—
210	#13133194	—	4	2	no	—
211	#13133194	—	4	2	no	—
212	C₂×C₄⋊Dic₅₃	—	4	2	no	—
213	C₂×C₄⋊Dic₅₃	—	4	2	no	—
214	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	C₂×#11719919	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	C₂³	1	1	yes	characteristic
234	C₂×#11719919	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×#11719919	C₂³	1	1	yes	characteristic
242	C₂×#11719919	C₂³	1	1	yes	characteristic
243	C₂×#11719919	C₂³	1	1	yes	characteristic
244	C₂×#11719919	C₂³	1	1	yes	characteristic
245	C₂×#11719919	C₂³	1	1	yes	characteristic
246	C₂×#11719919	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₅₃	—	4	2	no	—
248	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	#13133124	C₂³	1	1	yes	characteristic
279	#13133124	C₂³	1	1	yes	characteristic
280	#13133124	C₂³	1	1	yes	characteristic
281	#13133124	C₂³	1	1	yes	characteristic
282	#13133124	C₂³	1	1	yes	characteristic
283	#13133124	C₂³	1	1	yes	characteristic
284	#13133124	C₂³	1	1	yes	characteristic
285	#13133124	C₂³	1	1	yes	characteristic
286	#13133124	C₂³	1	1	yes	characteristic
287	#13133124	C₂³	1	1	yes	characteristic
288	#13133124	C₂³	1	1	yes	characteristic
289	#13133124	C₂³	1	1	yes	characteristic
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
325	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
326	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
327	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
328	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
329	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
331	#123×C₅₃	—	4	2	no	—
332	#120×C₅₃	—	4	2	no	—
333	C₄×D₄×C₅₃	—	2	4	no	—
334	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	C₂⁴×C₅₃	—	2	2	no	—
364	C₂⁴×C₅₃	—	2	2	no	—
365	C₂⁴×C₅₃	—	2	2	no	—
366	C₂⁴×C₅₃	—	2	2	no	—
367	C₂⁴×C₅₃	—	2	2	no	—
368	C₂⁴×C₅₃	—	4	1	no	—
369	C₂⁴×C₅₃	—	4	1	no	—
370	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₅₃	—	2	2	no	—
375	C₂×D₄×C₅₃	—	2	2	no	—
376	C₂×D₄×C₅₃	—	2	2	no	—
377	C₂×D₄×C₅₃	—	2	2	no	—
378	C₂×D₄×C₅₃	—	2	2	no	—
379	C₂×D₄×C₅₃	—	4	1	no	—
380	C₂×D₄×C₅₃	—	4	1	no	—
381	C₂×D₄×C₅₃	—	4	1	no	—
382	C₂×D₄×C₅₃	—	4	1	no	—
383	C₂²×C₄×C₅₃	—	2	2	no	—
384	C₂²×C₄×C₅₃	—	2	2	no	—
385	C₂²×C₄×C₅₃	—	2	2	no	—
386	C₂²×C₄×C₅₃	—	2	2	no	—
387	C₂²×C₄×C₅₃	—	4	1	no	—
388	C₂²×C₄×C₅₃	—	4	1	no	—
389	C₂²×C₄×C₅₃	—	4	1	no	—
390	C₂²×C₄×C₅₃	—	4	1	no	—
391	C₂²×C₄×C₅₃	#41	1	4	yes	—
392	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₅₃	—	2	2	no	—
404	C₂²×Dic₅₃	—	2	2	no	—
405	C₂²×Dic₅₃	—	2	2	no	—
406	C₂²×Dic₅₃	—	2	2	no	—
407	C₂²×Dic₅₃	—	2	2	no	—
408	C₂²×Dic₅₃	—	2	2	no	—
409	C₂²×Dic₅₃	—	2	2	no	—
410	C₂²×Dic₅₃	—	2	2	no	—
411	C₂²×Dic₅₃	—	2	2	no	—
412	C₂²×Dic₅₃	—	4	1	no	—
413	C₂²×Dic₅₃	—	4	1	no	—
414	C₂²×Dic₅₃	—	4	1	no	—
415	C₂²×Dic₅₃	—	4	1	no	—
416	C₂²×Dic₅₃	—	4	1	no	—
417	C₂²×Dic₅₃	—	4	1	no	—
418	C₂²×Dic₅₃	—	4	1	no	—
419	C₂²×Dic₅₃	—	4	1	no	—
420	C₂²×Dic₅₃	—	4	1	no	—
421	C₂²×Dic₅₃	—	4	1	no	—
422	C₂²×Dic₅₃	—	4	1	no	—
423	C₂²×Dic₅₃	—	4	1	no	—
424	C₂²×Dic₅₃	—	4	1	no	—
425	C₂²×Dic₅₃	—	4	1	no	—
426	C₂²×Dic₅₃	—	4	1	no	—
427	C₂²×Dic₅₃	—	4	16	no	—
428	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
430	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
431	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
433	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
434	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
435	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
436	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
437	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
438	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
439	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
440	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
441	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
444	C₂×Dic₁₀₆	—	2	2	no	—
445	C₂×Dic₁₀₆	—	2	2	no	—
446	C₂×Dic₁₀₆	—	4	1	no	—
447	C₂×Dic₁₀₆	—	4	1	no	—
448	C₂×Dic₁₀₆	—	4	1	no	—
449	C₂×Dic₁₀₆	—	4	1	no	—
450	C₂×Dic₁₀₆	—	4	1	no	—
451	C₂×Dic₁₀₆	—	4	1	no	—
452	C₂×Dic₁₀₆	—	4	1	no	—
453	C₄⋊C₄×C₅₃	—	2	2	no	—
454	C₄⋊C₄×C₅₃	—	4	1	no	—
455	C₄⋊C₄×C₅₃	—	4	1	no	—
456	C₄⋊C₄×C₅₃	—	4	1	no	—
457	C₄⋊C₄×C₅₃	—	4	1	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	2	no	—
461	C₂²⋊C₄×C₅₃	—	2	2	no	—
462	C₂²⋊C₄×C₅₃	—	2	2	no	—
463	C₂²⋊C₄×C₅₃	—	2	2	no	—
464	C₂²⋊C₄×C₅₃	—	2	2	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	—	2	2	no	—
467	C₂²⋊C₄×C₅₃	—	2	2	no	—
468	C₂²⋊C₄×C₅₃	—	4	1	no	—
469	C₂²⋊C₄×C₅₃	—	4	1	no	—
470	C₂²⋊C₄×C₅₃	—	4	1	no	—
471	C₂²⋊C₄×C₅₃	—	4	1	no	—
472	C₂²⋊C₄×C₅₃	—	4	1	no	—
473	C₂²⋊C₄×C₅₃	—	4	1	no	—
474	C₄²×C₅₃	—	2	2	no	—
475	C₂²⋊Dic₅₃	—	2	2	no	—
476	C₂²⋊Dic₅₃	—	2	2	no	—
477	C₂²⋊Dic₅₃	—	2	2	no	—
478	C₂²⋊Dic₅₃	—	2	2	no	—
479	C₂²⋊Dic₅₃	—	2	2	no	—
480	C₂²⋊Dic₅₃	—	2	2	no	—
481	C₂²⋊Dic₅₃	—	2	2	no	—
482	C₂²⋊Dic₅₃	—	2	2	no	—
483	C₂²⋊Dic₅₃	—	2	2	no	—
484	C₂²⋊Dic₅₃	—	2	2	no	—
485	C₂²⋊Dic₅₃	—	2	2	no	—
486	C₂²⋊Dic₅₃	—	4	1	no	—
487	C₂²⋊Dic₅₃	—	4	1	no	—
488	C₂²⋊Dic₅₃	—	4	1	no	—
489	C₂²⋊Dic₅₃	—	4	1	no	—
490	C₂²⋊Dic₅₃	—	4	1	no	—
491	C₂²⋊Dic₅₃	—	4	1	no	—
492	C₂²⋊Dic₅₃	—	4	1	no	—
493	C₂²⋊Dic₅₃	—	4	1	no	—
494	C₂²⋊Dic₅₃	—	4	1	no	—
495	C₂²⋊Dic₅₃	—	4	1	no	—
496	C₂²⋊Dic₅₃	—	4	1	no	—
497	C₂²⋊Dic₅₃	—	4	1	no	—
498	C₂²⋊Dic₅₃	—	4	1	no	—
499	C₄⋊Dic₅₃	—	2	2	no	—
500	C₄⋊Dic₅₃	—	2	2	no	—
501	C₄⋊Dic₅₃	—	2	2	no	—
502	C₄⋊Dic₅₃	—	4	1	no	—
503	C₄⋊Dic₅₃	—	4	1	no	—
504	C₄⋊Dic₅₃	—	4	1	no	—
505	C₄⋊Dic₅₃	—	4	1	no	—
506	C₄⋊Dic₅₃	—	4	1	no	—
507	C₄⋊Dic₅₃	—	4	1	no	—
508	C₄⋊Dic₅₃	—	4	1	no	—
509	C₄⋊Dic₅₃	—	4	1	no	—
510	C₄⋊Dic₅₃	—	4	1	no	—
511	C₄⋊Dic₅₃	—	4	1	no	—
512	C₄⋊Dic₅₃	—	4	1	no	—
513	C₄⋊Dic₅₃	—	4	1	no	—
514	#11719919	—	2	2	no	—
515	#11719919	—	2	2	no	—
516	#11719919	—	2	2	no	—
517	#11719919	—	2	2	no	—
518	#11719919	—	4	1	no	—
519	#11719919	—	4	1	no	—
520	#11719919	—	4	1	no	—
521	#11719919	—	4	1	no	—
522	#11719919	—	4	1	no	—
523	#11719919	—	4	1	no	—
524	#11719919	—	4	1	no	—
525	#11719919	—	4	1	no	—
526	#11719919	—	4	1	no	—
527	#11719919	—	4	1	no	—
528	#11719919	—	4	1	no	—
529	#11719919	—	4	1	no	—
530	#11719919	—	4	1	no	—
531	#11719919	—	4	1	no	—
532	C₄×Dic₅₃	—	4	1	no	—
533	C₄×Dic₅₃	—	4	1	no	—
534	C₄×Dic₅₃	—	4	1	no	—
535	C₄×Dic₅₃	—	4	1	no	—
536	C₄×Dic₅₃	—	4	1	no	—
537	C₄×Dic₅₃	—	4	1	no	—
538	C₂³×C₅₃	—	2	1	no	—
539	C₂³×C₅₃	—	2	1	no	—
540	C₂³×C₅₃	—	2	1	no	—
541	C₂³×C₅₃	—	2	1	no	—
542	C₂³×C₅₃	—	2	8	no	—
543	C₂³×C₅₃	—	2	1	no	—
544	C₂³×C₅₃	—	2	1	no	—
545	C₂³×C₅₃	—	2	1	no	—
546	C₂³×C₅₃	—	2	1	no	—
547	C₂³×C₅₃	—	2	1	no	—
548	C₂³×C₅₃	—	2	1	no	—
549	C₂³×C₅₃	—	2	1	no	—
550	C₂³×C₅₃	—	2	1	no	—
551	C₂³×C₅₃	—	2	1	no	—
552	C₂³×C₅₃	—	2	1	no	—
553	C₂³×C₅₃	—	2	1	no	—
554	C₂³×C₅₃	—	2	1	no	—
555	C₂³×C₅₃	—	2	1	no	—
556	C₂³×C₅₃	—	2	1	no	—
557	C₂³×C₅₃	—	2	1	no	—
558	C₂³×C₅₃	—	2	1	no	—
559	C₂³×C₅₃	—	2	1	no	—
560	C₂³×C₅₃	—	2	1	no	—
561	C₂³×C₅₃	—	2	1	no	—
562	C₂³×C₅₃	—	4	4	no	—
563	C₂³×C₅₃	—	4	4	no	—
564	C₂³×C₅₃	—	4	4	no	—
565	C₂³×C₅₃	—	4	4	no	—
566	C₂³×C₅₃	—	4	4	no	—
567	C₂³×C₅₃	—	4	4	no	—
568	C₂³×C₅₃	C₂×#41	1	2	yes	—
569	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
570	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
571	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
572	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
573	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
574	D₄×C₅₃	—	4	4	no	—
575	D₄×C₅₃	—	8	2	no	—
576	D₄×C₅₃	—	8	2	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	1	no	—
579	C₂×C₄×C₅₃	—	2	1	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	2	1	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	4	4	no	—
609	C₂×C₄×C₅₃	—	4	4	no	—
610	C₂×C₄×C₅₃	—	8	2	no	—
611	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
612	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
613	C₂×Dic₅₃	—	2	1	no	—
614	C₂×Dic₅₃	—	2	1	no	—
615	C₂×Dic₅₃	—	2	1	no	—
616	C₂×Dic₅₃	—	2	1	no	—
617	C₂×Dic₅₃	—	2	1	no	—
618	C₂×Dic₅₃	—	2	1	no	—
619	C₂×Dic₅₃	—	2	1	no	—
620	C₂×Dic₅₃	—	2	1	no	—
621	C₂×Dic₅₃	—	2	1	no	—
622	C₂×Dic₅₃	—	2	1	no	—
623	C₂×Dic₅₃	—	2	1	no	—
624	C₂×Dic₅₃	—	2	1	no	—
625	C₂×Dic₅₃	—	2	1	no	—
626	C₂×Dic₅₃	—	2	1	no	—
627	C₂×Dic₅₃	—	2	1	no	—
628	C₂×Dic₅₃	—	2	1	no	—
629	C₂×Dic₅₃	—	2	1	no	—
630	C₂×Dic₅₃	—	2	1	no	—
631	C₂×Dic₅₃	—	2	1	no	—
632	C₂×Dic₅₃	—	2	1	no	—
633	C₂×Dic₅₃	—	2	1	no	—
634	C₂×Dic₅₃	—	2	1	no	—
635	C₂×Dic₅₃	—	2	1	no	—
636	C₂×Dic₅₃	—	2	1	no	—
637	C₂×Dic₅₃	—	2	1	no	—
638	C₂×Dic₅₃	—	2	1	no	—
639	C₂×Dic₅₃	—	2	1	no	—
640	C₂×Dic₅₃	—	2	1	no	—
641	C₂×Dic₅₃	—	2	1	no	—
642	C₂×Dic₅₃	—	2	1	no	—
643	C₂×Dic₅₃	—	2	1	no	—
644	C₂×Dic₅₃	—	2	1	no	—
645	C₂×Dic₅₃	—	2	1	no	—
646	C₂×Dic₅₃	—	2	1	no	—
647	C₂×Dic₅₃	—	2	1	no	—
648	C₂×Dic₅₃	—	2	1	no	—
649	C₂×Dic₅₃	—	2	1	no	—
650	C₂×Dic₅₃	—	2	1	no	—
651	C₂×Dic₅₃	—	2	1	no	—
652	C₂×Dic₅₃	—	2	1	no	—
653	C₂×Dic₅₃	—	2	1	no	—
654	C₂×Dic₅₃	—	2	1	no	—
655	C₂×Dic₅₃	—	2	1	no	—
656	C₂×Dic₅₃	—	2	1	no	—
657	C₂×Dic₅₃	—	2	1	no	—
658	C₂×Dic₅₃	—	2	1	no	—
659	C₂×Dic₅₃	—	2	1	no	—
660	C₂×Dic₅₃	—	4	4	no	—
661	C₂×Dic₅₃	—	4	4	no	—
662	C₂×Dic₅₃	—	4	4	no	—
663	C₂×Dic₅₃	—	4	4	no	—
664	C₂×Dic₅₃	—	4	4	no	—
665	C₂×Dic₅₃	—	4	4	no	—
666	C₂×Dic₅₃	—	8	2	no	—
667	C₂×Dic₅₃	—	8	2	no	—
668	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
669	Dic₁₀₆	—	8	2	no	—
670	Dic₁₀₆	—	8	2	no	—
671	Dic₁₀₆	—	8	2	no	—
672	#36778	—	53	1	no	maximal, Sylow
673	C₂²×C₅₃	—	2	2	no	—
674	C₂²×C₅₃	—	2	2	no	—
675	C₂²×C₅₃	—	2	2	no	—
676	C₂²×C₅₃	—	2	2	no	—
677	C₂²×C₅₃	—	2	2	no	—
678	C₂²×C₅₃	—	2	2	no	—
679	C₂²×C₅₃	—	2	2	no	—
680	C₂²×C₅₃	—	2	2	no	—
681	C₂²×C₅₃	—	2	2	no	—
682	C₂²×C₅₃	—	2	2	no	—
683	C₂²×C₅₃	—	2	2	no	—
684	C₂²×C₅₃	—	2	2	no	—
685	C₂²×C₅₃	—	4	16	no	—
686	C₂²×C₅₃	—	4	1	no	—
687	C₂²×C₅₃	—	4	1	no	—
688	C₂²×C₅₃	—	4	1	no	—
689	C₂²×C₅₃	—	4	1	no	—
690	C₂²×C₅₃	—	4	1	no	—
691	C₂²×C₅₃	—	4	1	no	—
692	C₂²×C₅₃	—	4	1	no	—
693	C₂²×C₅₃	—	4	1	no	—
694	C₂²×C₅₃	—	4	1	no	—
695	C₂²×C₅₃	—	4	1	no	—
696	C₂²×C₅₃	—	4	1	no	—
697	C₂²×C₅₃	—	4	1	no	—
698	C₂²×C₅₃	—	4	1	no	—
699	C₂²×C₅₃	—	4	1	no	—
700	C₂²×C₅₃	—	4	1	no	—
701	C₂²×C₅₃	#542	1	4	yes	—
702	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
703	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
707	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
708	C₂²×C₅₃	#585	1	1	yes	characteristic
709	C₄×C₅₃	—	2	2	no	—
710	C₄×C₅₃	—	2	2	no	—
711	C₄×C₅₃	—	4	1	no	—
712	C₄×C₅₃	—	4	1	no	—
713	C₄×C₅₃	—	4	1	no	—
714	C₄×C₅₃	—	4	1	no	—
715	C₄×C₅₃	—	4	1	no	—
716	C₄×C₅₃	—	4	1	no	—
717	C₄×C₅₃	—	4	1	no	—
718	C₄×C₅₃	—	4	1	no	—
719	C₄×C₅₃	—	4	1	no	—
720	Dic₅₃	—	2	2	no	—
721	Dic₅₃	—	4	1	no	—
722	Dic₅₃	—	4	1	no	—
723	Dic₅₃	—	4	1	no	—
724	Dic₅₃	—	4	1	no	—
725	Dic₅₃	—	4	1	no	—
726	Dic₅₃	—	4	1	no	—
727	Dic₅₃	—	4	1	no	—
728	Dic₅₃	—	4	1	no	—
729	Dic₅₃	—	4	1	no	—
730	Dic₅₃	—	4	1	no	—
731	Dic₅₃	—	4	1	no	—
732	Dic₅₃	—	4	1	no	—
733	Dic₅₃	—	4	1	no	—
734	Dic₅₃	—	4	1	no	—
735	Dic₅₃	—	4	1	no	—
736	#2849	—	53	1	no	—
737	#2848	—	53	1	no	—
738	#2790	—	53	1	no	—
739	#2779	—	53	1	no	—
740	#2770	—	53	1	no	—
741	#2765	—	53	1	no	—
742	#2764	—	53	1	no	—
743	#2763	—	53	1	no	—
744	#2757	—	53	1	no	—
745	#2746	—	53	1	no	—
746	#2739	—	53	1	no	—
747	#2729	—	53	1	no	—
748	#2718	—	53	1	no	—
749	#2717	—	53	1	no	—
750	#2698	—	53	1	no	—
751	#2692	—	53	1	no	—
752	#2687	—	53	1	no	—
753	#2674	—	53	1	no	—
754	#2627	—	53	1	no	—
755	#2623	—	53	1	no	—
756	#2561	—	53	1	no	—
757	#2534	D₅₃	1	1	yes	characteristic
758	#2493	—	53	1	no	—
759	#2488	—	53	1	no	—
760	#2480	—	53	1	no	—
761	#2472	—	53	1	no	—
762	#2440	—	53	1	no	—
763	#2417	—	53	1	no	—
764	#2329	—	53	1	no	—
765	#2318	—	53	1	no	—
766	C₂×#385	—	53	1	no	—
767	C₂×C₅₃	—	2	4	no	—
768	C₂×C₅₃	—	4	2	no	—
769	C₂×C₅₃	—	4	2	no	—
770	C₂×C₅₃	—	8	1	no	—
771	C₂×C₅₃	C₂×#542	1	1	yes	characteristic
772	C₂×C₅₃	#3492	1	1	yes	characteristic
773	C₂×C₅₃	#3505	1	1	yes	characteristic
774	C₂×C₅₃	#3532	1	1	yes	characteristic
775	C₂×C₅₃	#3535	1	1	yes	characteristic
776	C₂×C₅₃	#3535	1	1	yes	characteristic
777	C₂×C₅₃	#3538	1	1	yes	characteristic
778	C₂⁴×C₄	—	53	1	no	—
779	C₂×C₄⋊Q₈	—	53	1	no	—
780	C₂×#126	—	53	1	no	—
781	C₂×#124	—	53	1	no	—
782	C₂×#123	—	53	1	no	—
783	C₂×#123	—	53	1	no	—
784	C₂×#123	C₂×D₅₃	1	1	yes	characteristic
785	C₂×C₂²⋊Q₈	—	53	1	no	—
786	C₂×C₂²⋊Q₈	—	53	1	no	—
787	C₂×C₂²⋊Q₈	—	53	1	no	—
788	C₂×C₂²⋊Q₈	—	53	1	no	—
789	C₂×C₂²⋊Q₈	—	53	1	no	—
790	C₂×C₂²⋊Q₈	—	53	1	no	—
791	C₂×#120	C₂×D₅₃	1	1	yes	characteristic
792	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
793	C₂²×C₄⋊C₄	—	53	1	no	—
794	C₂²×C₄⋊C₄	—	53	1	no	—
795	C₂²×C₂²⋊C₄	—	53	1	no	—
796	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
797	#401	—	53	1	no	—
798	#400	—	53	1	no	—
799	#400	—	53	1	no	—
800	#400	—	53	1	no	—
801	#400	—	53	1	no	—
802	#400	—	53	1	no	—
803	#400	—	53	1	no	—
804	#400	—	53	1	no	—
805	#400	—	53	1	no	—
806	#400	—	53	1	no	—
807	#399	—	53	1	no	—
808	#399	—	53	1	no	—
809	#398	—	53	1	no	—
810	#398	—	53	1	no	—
811	#398	—	53	1	no	—
812	#398	—	53	1	no	—
813	#398	—	53	1	no	—
814	#398	—	53	1	no	—
815	#398	—	53	1	no	—
816	#398	—	53	1	no	—
817	#398	—	53	1	no	—
818	#398	—	53	1	no	—
819	#397	—	53	1	no	—
820	#397	—	53	1	no	—
821	#397	—	53	1	no	—
822	#397	—	53	1	no	—
823	#397	—	53	1	no	—
824	#397	—	53	1	no	—
825	#397	—	53	1	no	—
826	#397	—	53	1	no	—
827	#397	—	53	1	no	—
828	#396	—	53	1	no	—
829	#396	—	53	1	no	—
830	#396	—	53	1	no	—
831	#396	C₂×D₅₃	1	1	yes	characteristic
832	#396	C₂×D₅₃	1	1	yes	characteristic
833	#395	—	53	1	no	—
834	#395	—	53	1	no	—
835	#395	—	53	1	no	—
836	#395	—	53	1	no	—
837	#394	—	53	1	no	—
838	#394	—	53	1	no	—
839	#394	C₂×D₅₃	1	1	yes	characteristic
840	#394	C₂×D₅₃	1	1	yes	characteristic
841	#393	—	53	1	no	—
842	#393	—	53	1	no	—
843	#393	—	53	1	no	—
844	#393	—	53	1	no	—
845	#391	—	53	1	no	—
846	#391	—	53	1	no	—
847	#391	—	53	1	no	—
848	#391	—	53	1	no	—
849	#390	—	53	1	no	—
850	#389	—	53	1	no	—
851	#389	—	53	1	no	—
852	#389	—	53	1	no	—
853	#389	—	53	1	no	—
854	#389	—	53	1	no	—
855	#388	—	53	1	no	—
856	#388	—	53	1	no	—
857	#388	—	53	1	no	—
858	#388	—	53	1	no	—
859	#388	—	53	1	no	—
860	#388	—	53	1	no	—
861	#388	—	53	1	no	—
862	#388	—	53	1	no	—
863	#388	—	53	1	no	—
864	#388	—	53	1	no	—
865	#388	—	53	1	no	—
866	#388	—	53	1	no	—
867	#388	—	53	1	no	—
868	#388	C₂×D₅₃	1	1	yes	characteristic
869	#388	C₂×D₅₃	1	1	yes	characteristic
870	#387	—	53	1	no	—
871	#387	—	53	1	no	—
872	#387	—	53	1	no	—
873	#387	—	53	1	no	—
874	#387	—	53	1	no	—
875	#387	—	53	1	no	—
876	#387	—	53	1	no	—
877	#387	—	53	1	no	—
878	#387	—	53	1	no	—
879	#386	—	53	1	no	—
880	#386	—	53	1	no	—
881	#386	—	53	1	no	—
882	#386	—	53	1	no	—
883	#386	—	53	1	no	—
884	#386	—	53	1	no	—
885	#386	C₂×D₅₃	1	1	yes	characteristic
886	#386	C₂×D₅₃	1	1	yes	characteristic
887	#385	—	53	1	no	—
888	#385	—	53	1	no	—
889	#385	—	53	1	no	—
890	#385	—	53	1	no	—
891	#385	—	53	1	no	—
892	#385	—	53	1	no	—
893	#385	—	53	1	no	—
894	#385	—	53	1	no	—
895	#385	—	53	1	no	—
896	#385	—	53	1	no	—
897	#385	—	53	1	no	—
898	#385	—	53	1	no	—
899	#385	—	53	1	no	—
900	#385	—	53	1	no	—
901	#385	—	53	1	no	—
902	#385	—	53	1	no	—
903	#385	—	53	1	no	—
904	#385	—	53	1	no	—
905	#385	—	53	1	no	—
906	#385	—	53	1	no	—
907	#384	—	53	1	no	—
908	#383	—	53	1	no	—
909	#383	—	53	1	no	—
910	#382	—	53	1	no	—
911	#382	—	53	1	no	—
912	#381	—	53	1	no	—
913	#381	—	53	1	no	—
914	#381	—	53	1	no	—
915	#381	—	53	1	no	—
916	#381	—	53	1	no	—
917	#381	C₂×D₅₃	1	1	yes	characteristic
918	#380	—	53	1	no	—
919	#380	—	53	1	no	—
920	#380	—	53	1	no	—
921	#380	—	53	1	no	—
922	#380	—	53	1	no	—
923	#380	—	53	1	no	—
924	#380	C₂×D₅₃	1	1	yes	characteristic
925	#379	—	53	1	no	—
926	#379	—	53	1	no	—
927	#379	C₂×D₅₃	1	1	yes	characteristic
928	C₄×C₂²⋊C₄	—	53	1	no	—
929	C₄×C₂²⋊C₄	—	53	1	no	—
930	C₄×C₂²⋊C₄	—	53	1	no	—
931	C₂×#95	—	53	1	no	—
932	C₂×#95	—	53	1	no	—
933	C₅₃	#36778	1	1	yes	characteristic, complemented, Sylow
934	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
935	C₂²×Q₈	—	53	1	no	—
936	C₂²×Q₈	—	53	1	no	—
937	C₂²×Q₈	—	53	1	no	—
938	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
939	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
940	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
941	C₂³×C₄	—	53	1	no	—
942	C₂³×C₄	—	53	1	no	—
943	C₂³×C₄	—	53	1	no	—
944	C₂³×C₄	—	53	1	no	—
945	C₂³×C₄	—	53	1	no	—
946	C₂³×C₄	—	53	1	no	—
947	C₂³×C₄	—	53	1	no	—
948	C₂³×C₄	—	53	1	no	—
949	C₂³×C₄	—	212	2	no	—
950	C₂³×C₄	—	212	2	no	—
951	C₂³×C₄	—	212	2	no	—
952	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
953	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
954	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
955	C₄⋊Q₈	—	212	2	no	—
956	#126	—	212	2	no	—
957	#124	—	212	2	no	—
958	#123	—	4	2	no	—
959	#123	—	212	2	no	—
960	#123	—	212	2	no	—
961	C₂²⋊Q₈	—	106	4	no	—
962	C₂²⋊Q₈	—	212	2	no	—
963	C₂²⋊Q₈	—	212	2	no	—
964	C₂²⋊Q₈	—	212	2	no	—
965	C₂²⋊Q₈	—	212	2	no	—
966	C₂²⋊Q₈	—	212	2	no	—
967	#120	—	4	2	no	—
968	C₄×D₄	—	2	4	no	—
969	C₂×C₄⋊C₄	—	53	1	no	—
970	C₂×C₄⋊C₄	—	53	1	no	—
971	C₂×C₄⋊C₄	—	53	1	no	—
972	C₂×C₄⋊C₄	—	53	1	no	—
973	C₂×C₄⋊C₄	—	53	1	no	—
974	C₂×C₄⋊C₄	—	53	1	no	—
975	C₂×C₄⋊C₄	—	53	1	no	—
976	C₂×C₄⋊C₄	—	53	1	no	—
977	C₂×C₄⋊C₄	—	53	1	no	—
978	C₂×C₄⋊C₄	—	53	1	no	—
979	C₂×C₄⋊C₄	—	53	1	no	—
980	C₂×C₄⋊C₄	—	53	1	no	—
981	C₂×C₄⋊C₄	—	53	1	no	—
982	C₂×C₄⋊C₄	—	53	1	no	—
983	C₂×C₄⋊C₄	—	53	1	no	—
984	C₂×C₄⋊C₄	—	53	1	no	—
985	C₂×C₄⋊C₄	—	53	1	no	—
986	C₂×C₄⋊C₄	—	53	1	no	—
987	C₂×C₄⋊C₄	—	53	1	no	—
988	C₂×C₄⋊C₄	—	53	1	no	—
989	C₂×C₄⋊C₄	—	53	1	no	—
990	C₂×C₄⋊C₄	—	53	1	no	—
991	C₂×C₄⋊C₄	—	53	1	no	—
992	C₂×C₄⋊C₄	—	53	1	no	—
993	C₂×C₄⋊C₄	—	53	1	no	—
994	C₂×C₄⋊C₄	—	53	1	no	—
995	C₂×C₄⋊C₄	—	53	1	no	—
996	C₂×C₄⋊C₄	—	53	1	no	—
997	C₂×C₄⋊C₄	—	53	1	no	—
998	C₂×C₄⋊C₄	—	53	1	no	—
999	C₂×C₄⋊C₄	—	53	1	no	—
1000	C₂×C₄⋊C₄	—	53	1	no	—
1001	C₂×C₄⋊C₄	—	53	1	no	—
1002	C₂×C₄⋊C₄	—	212	2	no	—
1003	C₂×C₄⋊C₄	—	212	2	no	—
1004	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1005	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1006	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1009	C₂×C₂²⋊C₄	—	2	4	no	—
1010	C₂×C₂²⋊C₄	—	53	1	no	—
1011	C₂×C₂²⋊C₄	—	53	1	no	—
1012	C₂×C₂²⋊C₄	—	53	1	no	—
1013	C₂×C₂²⋊C₄	—	53	1	no	—
1014	C₂×C₂²⋊C₄	—	53	1	no	—
1015	C₂×C₂²⋊C₄	—	53	1	no	—
1016	C₂×C₂²⋊C₄	—	53	1	no	—
1017	C₂×C₂²⋊C₄	—	53	1	no	—
1018	C₂×C₂²⋊C₄	—	53	1	no	—
1019	C₂×C₂²⋊C₄	—	53	1	no	—
1020	C₂×C₂²⋊C₄	—	53	1	no	—
1021	C₂×C₂²⋊C₄	—	53	1	no	—
1022	C₂×C₂²⋊C₄	—	53	1	no	—
1023	C₂×C₂²⋊C₄	—	53	1	no	—
1024	C₂×C₂²⋊C₄	—	53	1	no	—
1025	C₂×C₂²⋊C₄	—	53	1	no	—
1026	C₂×C₂²⋊C₄	—	53	1	no	—
1027	C₂×C₂²⋊C₄	—	53	1	no	—
1028	C₂×C₂²⋊C₄	—	53	1	no	—
1029	C₂×C₂²⋊C₄	—	53	1	no	—
1030	C₂×C₂²⋊C₄	—	53	1	no	—
1031	C₂×C₂²⋊C₄	—	53	1	no	—
1032	C₂×C₂²⋊C₄	—	53	1	no	—
1033	C₂×C₂²⋊C₄	—	53	1	no	—
1034	C₂×C₂²⋊C₄	—	212	2	no	—
1035	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1037	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1038	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1043	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1044	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1045	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1046	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1047	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1048	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1049	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1050	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1051	C₂×C₄²	—	53	1	no	—
1052	C₂×C₄²	—	53	1	no	—
1053	C₂×C₄²	—	53	1	no	—
1054	C₂×C₄²	—	53	1	no	—
1055	C₂×C₄²	—	53	1	no	—
1056	C₂×C₄²	—	53	1	no	—
1057	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1058	#95	—	53	1	no	—
1059	#95	—	53	1	no	—
1060	#95	—	53	1	no	—
1061	#95	—	53	1	no	—
1062	#95	—	53	1	no	—
1063	#95	—	53	1	no	—
1064	#95	—	53	1	no	—
1065	#95	—	53	1	no	—
1066	#95	—	53	1	no	—
1067	#95	—	53	1	no	—
1068	#95	—	53	1	no	—
1069	#95	—	53	1	no	—
1070	#95	—	53	1	no	—
1071	#95	—	53	1	no	—
1072	#95	—	53	1	no	—
1073	#95	—	53	1	no	—
1074	#95	—	53	1	no	—
1075	#95	—	53	1	no	—
1076	#95	—	53	1	no	—
1077	#95	—	53	1	no	—
1078	#95	—	53	1	no	—
1079	#95	—	53	1	no	—
1080	#95	—	53	1	no	—
1081	#95	—	53	1	no	—
1082	#95	—	53	1	no	—
1083	#95	—	53	1	no	—
1084	#95	—	53	1	no	—
1085	#95	—	53	1	no	—
1086	#95	—	53	1	no	—
1087	#95	—	53	1	no	—
1088	#95	—	53	1	no	—
1089	#95	—	53	1	no	—
1090	#95	—	53	1	no	—
1091	#95	—	53	1	no	—
1092	#95	—	53	1	no	—
1093	#95	—	53	1	no	—
1094	#95	—	53	1	no	—
1095	#95	—	53	1	no	—
1096	#95	—	53	1	no	—
1097	#95	—	53	1	no	—
1098	#95	—	53	1	no	—
1099	#95	—	53	1	no	—
1100	#95	—	53	1	no	—
1101	#95	—	53	1	no	—
1102	#95	—	53	1	no	—
1103	#95	—	53	1	no	—
1104	#95	C₂²×D₅₃	1	1	yes	characteristic
1105	#95	C₂²×D₅₃	1	1	yes	characteristic
1106	#95	C₂²×D₅₃	1	1	yes	characteristic
1107	#95	C₂²×D₅₃	1	1	yes	characteristic
1108	#95	C₂²×D₅₃	1	1	yes	characteristic
1109	#95	C₂²×D₅₃	1	1	yes	characteristic
1110	C₂⁴	—	2	2	no	—
1111	C₂⁴	—	2	2	no	—
1112	C₂⁴	—	2	2	no	—
1113	C₂⁴	—	2	2	no	—
1114	C₂⁴	—	2	2	no	—
1115	C₂⁴	—	4	1	no	—
1116	C₂⁴	—	4	1	no	—
1117	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1118	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1119	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1120	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1121	C₂×Q₈	—	106	2	no	—
1122	C₂×Q₈	—	106	2	no	—
1123	C₂×Q₈	—	212	1	no	—
1124	C₂×Q₈	—	212	1	no	—
1125	C₂×Q₈	—	212	1	no	—
1126	C₂×Q₈	—	212	1	no	—
1127	C₂×Q₈	—	212	1	no	—
1128	C₂×Q₈	—	212	1	no	—
1129	C₂×Q₈	—	212	1	no	—
1130	C₂×D₄	—	2	2	no	—
1131	C₂×D₄	—	2	2	no	—
1132	C₂×D₄	—	2	2	no	—
1133	C₂×D₄	—	2	2	no	—
1134	C₂×D₄	—	2	2	no	—
1135	C₂×D₄	—	4	1	no	—
1136	C₂×D₄	—	4	1	no	—
1137	C₂×D₄	—	4	1	no	—
1138	C₂×D₄	—	4	1	no	—
1139	C₂²×C₄	—	2	2	no	—
1140	C₂²×C₄	—	2	2	no	—
1141	C₂²×C₄	—	2	2	no	—
1142	C₂²×C₄	—	2	2	no	—
1143	C₂²×C₄	—	4	1	no	—
1144	C₂²×C₄	—	4	1	no	—
1145	C₂²×C₄	—	4	1	no	—
1146	C₂²×C₄	—	4	1	no	—
1147	C₂²×C₄	—	53	1	no	—
1148	C₂²×C₄	—	53	1	no	—
1149	C₂²×C₄	—	53	1	no	—
1150	C₂²×C₄	—	53	1	no	—
1151	C₂²×C₄	—	53	1	no	—
1152	C₂²×C₄	—	53	1	no	—
1153	C₂²×C₄	—	53	1	no	—
1154	C₂²×C₄	—	53	1	no	—
1155	C₂²×C₄	—	53	1	no	—
1156	C₂²×C₄	—	53	1	no	—
1157	C₂²×C₄	—	53	1	no	—
1158	C₂²×C₄	—	53	1	no	—
1159	C₂²×C₄	—	53	1	no	—
1160	C₂²×C₄	—	53	1	no	—
1161	C₂²×C₄	—	53	1	no	—
1162	C₂²×C₄	—	53	1	no	—
1163	C₂²×C₄	—	106	2	no	—
1164	C₂²×C₄	—	106	2	no	—
1165	C₂²×C₄	—	106	2	no	—
1166	C₂²×C₄	—	106	2	no	—
1167	C₂²×C₄	—	106	2	no	—
1168	C₂²×C₄	—	106	2	no	—
1169	C₂²×C₄	—	106	2	no	—
1170	C₂²×C₄	—	106	2	no	—
1171	C₂²×C₄	—	106	2	no	—
1172	C₂²×C₄	—	212	1	no	—
1173	C₂²×C₄	—	212	1	no	—
1174	C₂²×C₄	—	212	1	no	—
1175	C₂²×C₄	—	212	1	no	—
1176	C₂²×C₄	—	212	1	no	—
1177	C₂²×C₄	—	212	1	no	—
1178	C₂²×C₄	—	212	1	no	—
1179	C₂²×C₄	—	212	1	no	—
1180	C₂²×C₄	—	212	1	no	—
1181	C₂²×C₄	—	212	1	no	—
1182	C₂²×C₄	—	212	1	no	—
1183	C₂²×C₄	—	212	1	no	—
1184	C₂²×C₄	—	212	1	no	—
1185	C₂²×C₄	—	212	1	no	—
1186	C₂²×C₄	—	212	1	no	—
1187	C₂²×C₄	—	212	16	no	—
1188	C₂²×C₄	#11719947	1	4	yes	—
1189	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1190	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1191	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1192	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1193	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1194	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1195	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1196	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1197	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1198	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1199	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1200	C₄⋊C₄	—	2	2	no	—
1201	C₄⋊C₄	—	4	1	no	—
1202	C₄⋊C₄	—	4	1	no	—
1203	C₄⋊C₄	—	4	1	no	—
1204	C₄⋊C₄	—	4	1	no	—
1205	C₄⋊C₄	—	106	2	no	—
1206	C₄⋊C₄	—	106	2	no	—
1207	C₄⋊C₄	—	106	2	no	—
1208	C₄⋊C₄	—	106	2	no	—
1209	C₄⋊C₄	—	106	2	no	—
1210	C₄⋊C₄	—	106	2	no	—
1211	C₄⋊C₄	—	106	2	no	—
1212	C₄⋊C₄	—	212	1	no	—
1213	C₄⋊C₄	—	212	1	no	—
1214	C₄⋊C₄	—	212	1	no	—
1215	C₄⋊C₄	—	212	1	no	—
1216	C₄⋊C₄	—	212	1	no	—
1217	C₄⋊C₄	—	212	1	no	—
1218	C₄⋊C₄	—	212	1	no	—
1219	C₄⋊C₄	—	212	1	no	—
1220	C₄⋊C₄	—	212	1	no	—
1221	C₄⋊C₄	—	212	1	no	—
1222	C₄⋊C₄	—	212	1	no	—
1223	C₄⋊C₄	—	212	1	no	—
1224	C₄⋊C₄	—	212	1	no	—
1225	C₄⋊C₄	—	212	1	no	—
1226	C₄⋊C₄	—	212	1	no	—
1227	C₄⋊C₄	—	212	1	no	—
1228	C₄⋊C₄	—	212	1	no	—
1229	C₄⋊C₄	—	212	1	no	—
1230	C₄⋊C₄	—	212	1	no	—
1231	C₄⋊C₄	—	212	1	no	—
1232	C₄⋊C₄	—	212	1	no	—
1233	C₄⋊C₄	—	212	1	no	—
1234	C₄⋊C₄	—	212	1	no	—
1235	C₄⋊C₄	—	212	1	no	—
1236	C₄⋊C₄	—	212	1	no	—
1237	C₄⋊C₄	—	212	1	no	—
1238	C₂²⋊C₄	—	2	2	no	—
1239	C₂²⋊C₄	—	2	2	no	—
1240	C₂²⋊C₄	—	2	2	no	—
1241	C₂²⋊C₄	—	2	2	no	—
1242	C₂²⋊C₄	—	2	2	no	—
1243	C₂²⋊C₄	—	2	2	no	—
1244	C₂²⋊C₄	—	2	2	no	—
1245	C₂²⋊C₄	—	2	2	no	—
1246	C₂²⋊C₄	—	2	2	no	—
1247	C₂²⋊C₄	—	2	2	no	—
1248	C₂²⋊C₄	—	4	1	no	—
1249	C₂²⋊C₄	—	4	1	no	—
1250	C₂²⋊C₄	—	4	1	no	—
1251	C₂²⋊C₄	—	4	1	no	—
1252	C₂²⋊C₄	—	4	1	no	—
1253	C₂²⋊C₄	—	4	1	no	—
1254	C₂²⋊C₄	—	106	2	no	—
1255	C₂²⋊C₄	—	106	2	no	—
1256	C₂²⋊C₄	—	106	2	no	—
1257	C₂²⋊C₄	—	106	2	no	—
1258	C₂²⋊C₄	—	106	2	no	—
1259	C₂²⋊C₄	—	106	2	no	—
1260	C₂²⋊C₄	—	106	2	no	—
1261	C₂²⋊C₄	—	106	2	no	—
1262	C₂²⋊C₄	—	106	2	no	—
1263	C₂²⋊C₄	—	106	2	no	—
1264	C₂²⋊C₄	—	106	2	no	—
1265	C₂²⋊C₄	—	212	1	no	—
1266	C₂²⋊C₄	—	212	1	no	—
1267	C₂²⋊C₄	—	212	1	no	—
1268	C₂²⋊C₄	—	212	1	no	—
1269	C₂²⋊C₄	—	212	1	no	—
1270	C₂²⋊C₄	—	212	1	no	—
1271	C₂²⋊C₄	—	212	1	no	—
1272	C₂²⋊C₄	—	212	1	no	—
1273	C₂²⋊C₄	—	212	1	no	—
1274	C₂²⋊C₄	—	212	1	no	—
1275	C₂²⋊C₄	—	212	1	no	—
1276	C₂²⋊C₄	—	212	1	no	—
1277	C₂²⋊C₄	—	212	1	no	—
1278	C₄²	—	2	2	no	—
1279	C₄²	—	212	1	no	—
1280	C₄²	—	212	1	no	—
1281	C₄²	—	212	1	no	—
1282	C₄²	—	212	1	no	—
1283	C₄²	—	212	1	no	—
1284	C₄²	—	212	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	2	8	no	—
1290	C₂³	—	2	1	no	—
1291	C₂³	—	2	1	no	—
1292	C₂³	—	2	1	no	—
1293	C₂³	—	2	1	no	—
1294	C₂³	—	2	1	no	—
1295	C₂³	—	2	1	no	—
1296	C₂³	—	2	1	no	—
1297	C₂³	—	2	1	no	—
1298	C₂³	—	2	1	no	—
1299	C₂³	—	2	1	no	—
1300	C₂³	—	2	1	no	—
1301	C₂³	—	2	1	no	—
1302	C₂³	—	2	1	no	—
1303	C₂³	—	2	1	no	—
1304	C₂³	—	2	1	no	—
1305	C₂³	—	2	1	no	—
1306	C₂³	—	2	1	no	—
1307	C₂³	—	2	1	no	—
1308	C₂³	—	2	1	no	—
1309	C₂³	—	4	4	no	—
1310	C₂³	—	4	4	no	—
1311	C₂³	—	4	4	no	—
1312	C₂³	—	4	4	no	—
1313	C₂³	—	4	4	no	—
1314	C₂³	—	4	4	no	—
1315	C₂³	C₂×#11719947	1	2	yes	—
1316	C₂³	#13133262	1	2	yes	—
1317	C₂³	#13133263	1	2	yes	—
1318	C₂³	#13133264	1	2	yes	—
1319	C₂³	#13133264	1	2	yes	—
1320	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1321	Q₈	—	424	2	no	—
1322	Q₈	—	424	2	no	—
1323	Q₈	—	424	2	no	—
1324	D₄	—	4	4	no	—
1325	D₄	—	8	2	no	—
1326	D₄	—	8	2	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	4	4	no	—
1359	C₂×C₄	—	4	4	no	—
1360	C₂×C₄	—	8	2	no	—
1361	C₂×C₄	—	53	2	no	—
1362	C₂×C₄	—	106	1	no	—
1363	C₂×C₄	—	106	1	no	—
1364	C₂×C₄	—	106	1	no	—
1365	C₂×C₄	—	106	1	no	—
1366	C₂×C₄	—	106	1	no	—
1367	C₂×C₄	—	106	1	no	—
1368	C₂×C₄	—	106	1	no	—
1369	C₂×C₄	—	106	1	no	—
1370	C₂×C₄	—	106	1	no	—
1371	C₂×C₄	—	106	1	no	—
1372	C₂×C₄	—	106	1	no	—
1373	C₂×C₄	—	106	1	no	—
1374	C₂×C₄	—	106	1	no	—
1375	C₂×C₄	—	106	1	no	—
1376	C₂×C₄	—	106	1	no	—
1377	C₂×C₄	—	106	1	no	—
1378	C₂×C₄	—	106	1	no	—
1379	C₂×C₄	—	106	1	no	—
1380	C₂×C₄	—	106	1	no	—
1381	C₂×C₄	—	106	1	no	—
1382	C₂×C₄	—	106	1	no	—
1383	C₂×C₄	—	106	1	no	—
1384	C₂×C₄	—	106	1	no	—
1385	C₂×C₄	—	106	1	no	—
1386	C₂×C₄	—	106	1	no	—
1387	C₂×C₄	—	106	1	no	—
1388	C₂×C₄	—	106	1	no	—
1389	C₂×C₄	—	106	1	no	—
1390	C₂×C₄	—	106	1	no	—
1391	C₂×C₄	—	106	1	no	—
1392	C₂×C₄	—	106	1	no	—
1393	C₂×C₄	—	106	1	no	—
1394	C₂×C₄	—	106	1	no	—
1395	C₂×C₄	—	106	1	no	—
1396	C₂×C₄	—	106	1	no	—
1397	C₂×C₄	—	106	1	no	—
1398	C₂×C₄	—	106	1	no	—
1399	C₂×C₄	—	106	1	no	—
1400	C₂×C₄	—	106	1	no	—
1401	C₂×C₄	—	106	1	no	—
1402	C₂×C₄	—	106	1	no	—
1403	C₂×C₄	—	106	1	no	—
1404	C₂×C₄	—	106	1	no	—
1405	C₂×C₄	—	106	1	no	—
1406	C₂×C₄	—	106	1	no	—
1407	C₂×C₄	—	106	1	no	—
1408	C₂×C₄	—	106	1	no	—
1409	C₂×C₄	—	424	2	no	—
1410	C₂×C₄	—	424	2	no	—
1411	C₂×C₄	—	212	4	no	—
1412	C₂×C₄	—	212	4	no	—
1413	C₂×C₄	—	212	4	no	—
1414	C₂×C₄	—	212	4	no	—
1415	C₂×C₄	—	212	4	no	—
1416	C₂×C₄	—	212	4	no	—
1417	C₂×C₄	C₂×#11719947	1	2	yes	—
1418	C₂×C₄	C₂×#11719947	1	2	yes	—
1419	C₂²	—	2	2	no	—
1420	C₂²	—	2	2	no	—
1421	C₂²	—	2	2	no	—
1422	C₂²	—	2	2	no	—
1423	C₂²	—	2	2	no	—
1424	C₂²	—	2	2	no	—
1425	C₂²	—	2	2	no	—
1426	C₂²	—	2	2	no	—
1427	C₂²	—	2	2	no	—
1428	C₂²	—	2	2	no	—
1429	C₂²	—	2	2	no	—
1430	C₂²	—	2	2	no	—
1431	C₂²	—	4	16	no	—
1432	C₂²	—	4	1	no	—
1433	C₂²	—	4	1	no	—
1434	C₂²	—	4	1	no	—
1435	C₂²	—	4	1	no	—
1436	C₂²	—	4	1	no	—
1437	C₂²	—	4	1	no	—
1438	C₂²	—	4	1	no	—
1439	C₂²	—	4	1	no	—
1440	C₂²	—	4	1	no	—
1441	C₂²	—	4	1	no	—
1442	C₂²	—	4	1	no	—
1443	C₂²	—	4	1	no	—
1444	C₂²	—	4	1	no	—
1445	C₂²	—	4	1	no	—
1446	C₂²	—	4	1	no	—
1447	C₂²	#16811240	1	4	yes	—
1448	C₂²	C₂²×#11719947	1	1	yes	characteristic
1449	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1450	C₂²	C₂×#13133262	1	1	yes	characteristic
1451	C₂²	C₂×#13133263	1	1	yes	characteristic
1452	C₂²	C₂×#13133264	1	1	yes	characteristic
1453	C₂²	C₂×#13133264	1	1	yes	characteristic
1454	C₂²	#16811458	1	1	yes	characteristic
1455	C₄	—	2	2	no	—
1456	C₄	—	2	2	no	—
1457	C₄	—	4	1	no	—
1458	C₄	—	4	1	no	—
1459	C₄	—	4	1	no	—
1460	C₄	—	4	1	no	—
1461	C₄	—	4	1	no	—
1462	C₄	—	4	1	no	—
1463	C₄	—	4	1	no	—
1464	C₄	—	4	1	no	—
1465	C₄	—	4	1	no	—
1466	C₄	—	106	2	no	—
1467	C₄	—	212	1	no	—
1468	C₄	—	212	1	no	—
1469	C₄	—	212	1	no	—
1470	C₄	—	212	1	no	—
1471	C₄	—	212	1	no	—
1472	C₄	—	212	1	no	—
1473	C₄	—	212	1	no	—
1474	C₄	—	212	1	no	—
1475	C₄	—	212	1	no	—
1476	C₄	—	212	1	no	—
1477	C₄	—	212	1	no	—
1478	C₄	—	212	1	no	—
1479	C₄	—	212	1	no	—
1480	C₄	—	212	1	no	—
1481	C₄	—	212	1	no	—
1482	C₂	—	2	4	no	—
1483	C₂	—	4	2	no	—
1484	C₂	—	4	2	no	—
1485	C₂	—	8	1	no	—
1486	C₂	C₂×#16811240	1	1	yes	characteristic
1487	C₂	#20288421	1	1	yes	characteristic
1488	C₂	#20288552	1	1	yes	characteristic
1489	C₂	#20288864	1	1	yes	characteristic
1490	C₂	#20288912	1	1	yes	characteristic
1491	C₂	#20288920	1	1	yes	characteristic
1492	C₂	#20288955	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2534	C₂
prime radical	C₂×#120×C₅₃	C₂²
hypercenter	#2534	D₅₃
hypocenter	C₅₃	#36778
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2534

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #20283000	C₂	semidirect
3. #20282478	C₂	semidirect
4. #20282341	C₂	semidirect
5. #20282223	C₂	semidirect
6. #20282156	C₂	semidirect
7. #20282140	C₂	semidirect
8. #20282131	C₂	semidirect
9. #20282054	C₂	semidirect
10. #20281903	C₂	semidirect
11. #20281806	C₂	semidirect
12. #20281690	C₂	semidirect
13. #20281567	C₂	semidirect
14. #20281553	C₂	semidirect
15. #20281287	C₂	semidirect
16. #20281215	C₂	semidirect
17. #20281140	C₂	semidirect
18. #20280998	C₂	semidirect
19. #20280532	C₂	semidirect
20. #20280497	C₂	semidirect
21. #20279873	C₂	semidirect
22. #20279096	C₂	semidirect
23. #20279045	C₂	semidirect
24. #20278960	C₂	semidirect
26. #20278418	C₂	semidirect
27. #20278166	C₂	semidirect
28. #20277445	C₂	semidirect
29. #20277348	C₂	semidirect
30. C₂×#16810498	C₂	semidirect
33. C₂×#13133216	C₂²	semidirect
39. C₂×#13133196	C₂²	semidirect
47. C₅₃⋊#401	C₂²	semidirect
48. #16810565	C₂²	semidirect
49. #16810565	C₂²	semidirect
50. #16810565	C₂²	semidirect
51. #16810564	C₂²	semidirect
52. #16810563	C₂²	semidirect
53. #16810562	C₂²	semidirect
54. #16810562	C₂²	semidirect
55. #16810561	C₂²	semidirect
56. #16810561	C₂²	semidirect
57. #16810559	C₂²	semidirect
58. #16810559	C₂²	semidirect
59. #16810557	C₂²	semidirect
60. #16810557	C₂²	semidirect
61. #16810557	C₂²	semidirect
62. #16810557	C₂²	semidirect
63. #16810556	C₂²	semidirect
64. #16810556	C₂²	semidirect
65. #16810555	C₂²	semidirect
66. #16810555	C₂²	semidirect
67. #16810553	C₂²	semidirect
68. #16810553	C₂²	semidirect
75. #16810548	C₂²	semidirect
76. #16810548	C₂²	semidirect
77. #16810548	C₂²	semidirect
79. #16810546	C₂²	semidirect
80. #16810546	C₂²	semidirect
81. #16810544	C₂²	semidirect
82. #16810544	C₂²	semidirect
83. #16810544	C₂²	semidirect
84. #16810544	C₂²	semidirect
90. #16810535	C₂²	semidirect
91. #16810529	C₂²	semidirect
92. #16810528	C₂²	semidirect
93. #16810527	C₂²	semidirect
94. #16810527	C₂²	semidirect
96. #16810522	C₂²	semidirect
97. #16810521	C₂²	semidirect
98. #16810519	C₂²	semidirect
99. #16810518	C₂²	semidirect
100. #16810518	C₂²	semidirect
108. #16810517	C₂²	semidirect
109. #16810517	C₂²	semidirect
111. #16810516	C₂²	semidirect
112. #16810516	C₂²	semidirect
114. #16810510	C₂²	semidirect
115. #16810509	C₂²	semidirect
116. #16810509	C₂²	semidirect
117. #16810508	C₂²	semidirect
118. #16810508	C₂²	semidirect
119. #16810508	C₂²	semidirect
120. #16810505	C₂²	semidirect
121. #16810504	C₂²	semidirect
122. #16810504	C₂²	semidirect
149. #16810492	C₂²	semidirect
150. #16810491	C₂²	semidirect
151. #16810490	C₂²	semidirect
152. #16810489	C₂²	semidirect
153. #16810488	C₂²	semidirect
156. #16810486	C₂²	semidirect
159. #16810483	C₂²	semidirect
160. #16810483	C₂²	semidirect
933. C₅₃	#36778	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20283005	2
#20283000	2
#20282478	2
#20282341	2
#20282223	2
#20282156	2
#20282140	2
#20282131	2
#20282054	2
#20281903	2
#20281806	2
#20281690	2
#20281567	2
#20281553	2
#20281287	2
#20281215	2
#20281140	2
#20280998	2
#20280532	2
#20280497	2
#20279873	2
#20279096	2
#20279045	2
#20278960	2
#20278840	2
#20278418	2
#20278166	2
#20277445	2
#20277348	2
C₂×#16810498	2
C₅₃×#2534	2
#36778	53